English football has suffered many blights in its 146-year journey from amateur upper-class pastime to global entertainment industry, and along with fans fighting, one of the most persistent has been a tendency to generalise about it. So in the 1970s and 1980s, the game was characterised as a war zone plagued by hooliganism, while since its rehabilitation in the early 1990s football matches have been portrayed as completely cleansed of that menace – as fun, wholesome events to which all parents should feel confident about taking their kids.

There is a hard core of truth in both portrayals, but neither is the full story, as regular football fans, the football authorities, police and the government all agree. The 1970s and 1980s were indeed savaged all too often by fighting, which ultimately shamed the game's history with the horror of Heysel, but it did not happen all the time and in truth, it was always a minority who did any actual fighting. They dominated the experience at too many matches partly because policing was less well-organised than today, partly because thousands of fans around them seemed to glory in it, even if they did not become seriously involved.

Hooliganism within and outside grounds has dramatically declined since the early 1990s, and people do generally feel safe, barely considering the threat of violence at matches. That becalminghas played a major part in people flocking back to football in huge numbers not seen since the mid-1960s, along with modernised grounds, the media's more positive portrayal of the game, and the advent of huge new money in the Premier League which has paid for many of the world's stars to play here.

It is, though, not the whole truth to paint modern football as a shiny, happy carnival of multi-ethnic family fun in which hooliganism is a distant memory. While violence like last night's is, thankfully, extremely rare now at matches, there are still small groups of men who engage occasionally in the bizarre, dismal ritual of arranging fights away from grounds to avoid today's more intense policing.

Many lads who considered themselves "handy" back in the day are still supporters, and although they have expanded into middle age and generally "retired", they can still be roused into action in extreme circumstances like an incendiary meeting between West Ham and Millwall. Some fans of a certain late-30s to mid-50s vintage do not seem even to realise how nasty the old fighting songs sound when rolled out regularly and tediously in football grounds today.

Football hooliganism fell away for many reasons. There was a palpable feeling in the late 1980s, after so many people had died at grounds, that it had all gone too far, and many fans improved their behaviour. The police arrested some of the "top boys" at many clubs, the new all-seater stadiums dispersed groups to fixed seats and incorporated CCTV which can identify troublemakers.

More broadly, the culture changed. Football was celebrated, not vilified, in the media, and fans reclaimed its joys. The game has also become a more packaged, "leisure" experience, with fans shopping in megastores before games or watching big screens, not being left to make their own entertainment. Tickets are also more expensive, eye-wateringly so at some Premier League clubs, which has priced out much of the younger generation, some of whom might be more inclined to fight.

Official figures buttress the experience of diminished violence at football. In 1988-89 there were 6,185 football-related arrests in England's four professional divisions; in 2007-08, among crowds vastly larger, there were 3,616. Inside and outside grounds there were an average 1.21 arrests at a match, representing 0.01% of all supporters, and less than a 10th of the arrests were for violent offences. The police have largely reduced their presence and quietly withdrawn from many matches – 41% of matches in 2007-08 were police-free.

The Home Office is convinced that banning orders, introduced after the running battles seen at the European Championship in 2000, have been particularly effective. The most recent figures, for the 2007-08 season, show that 3,172 banning orders were in place.

"We don't subscribe to the idea that hooligans are not genuine fans, because that isn't true," a Home Office source explained. "These people do not want to be banned from the football experience, which is an important part of their lives. The exclusion of those who do cause trouble helps to stop people around them, who might become involved, crossing that line."

In the wake of last night's violence, the football authorities, police, government and the Football Supporters' Federation have all been emphasising the general reduction in hooliganism over the last 20 years. They are also realistic enough to accept there remains a risk of it happening, which does not come much higher than a midweek, floodlit cup tie between West Ham and Millwall.